Non-custodial refers to the situation in which the private keys to a Bitcoin wallet are not stored on a server or with a company that operates the wallet. This shifts the onus of protecting the wallet fully on the operator of the wallet. Non-custodial wallets provide more security because the private keys for the wallet can be more easily protected. But with more security comes more responsibility. With non-custodial wallets, the responsibility of properly protecting and storing the private key falls completely on the user.
- What are cryptocurrency custody solutions? – Investopedia